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  <h1 id="MathNet_Numerics_LinearAlgebra" data-uid="MathNet.Numerics.LinearAlgebra" class="text-break">Namespace MathNet.Numerics.LinearAlgebra
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    <h3 id="classes">Classes
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      <h4><a class="xref" href="MathNet.Numerics.LinearAlgebra.NamespaceDoc.html">NamespaceDoc</a></h4>
      <section><p>This namespace is a port of the 
<a href="http://math.nist.gov/javanumerics/jama/">JAMA library</a>.</p>
<p>The <code>MathNet.Numerics.LinearAlgebra</code> provides the fundamental operations 
of numerical linear algebra.  Various constructors create Matrices from two 
dimensional arrays of double precision floating point numbers.  Various &quot;gets&quot; 
and &quot;sets&quot; provide access to submatrices and matrix elements.  Several methods 
implement basic matrix arithmetic, including matrix addition and
multiplication, matrix norms, and element-by-element array operations.
Methods for reading and printing matrices are also included.  All the
operations in this version of the Matrix Class involve real matrices.
Complex matrices may be handled in a future version.</p>
<p>Five fundamental matrix decompositions, which consist of pairs or triples
of matrices, permutation vectors, and the like, produce results in five
decomposition classes.  These decompositions are accessed by the Matrix
class to compute solutions of simultaneous linear equations, determinants,
inverses and other matrix functions.</p>
<p>The five decompositions are:<br></p>
<ul>
<li>Cholesky Decomposition of symmetric, positive definite matrices.</li>
<li>LU Decomposition of rectangular matrices.</li>
<li>QR Decomposition of rectangular matrices.</li>
<li>Singular Value Decomposition of rectangular matrices.</li>
<li>Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.</li>
</ul>
<p><strong>Example of use:</strong> Solve a linear system <code>A x = b</code> and compute the residual norm, 
<code>||b - A x||</code>.</p>
<pre><code>double[,] vals = {{1.,2.,3.},{4.,5.,6.},{7.,8.,10.}};
Matrix a = new Matrix(vals);
Matrix b = Matrix.Random(3,1);
Matrix x = a.Solve(b);
Matrix r = a * x - b;
double rnorm = r.NormInf();</code></pre>
<p>Author: The MathWorks, Inc. and the National Institute of Standards and Technology (5 August 1998).</p>
<p>Port: Joannes Vermorel (2004).</p>
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